Modelling of structural complexity in sedimentary basins: The role of pre-existing faults in thrust tectonics

97

Tectonophysics, 226 (1993) 97-112

Elsevier Science Publishers B.V., Amsterdam

Modelling of structural complexity in sedimentary basins: the role of pre-existing faults in thrust tectonics W. Sassi, B. Colletta, Institut Fraqais

P. BalC and T. Paquereau

du P&role, I-4 Avenue Bois P&au, 92600 Rueil Malmaison Ceder, France

(Received October 15,1992; revised version accepted March 9,1993)

ABSTRACT

Analogue and numerical models have been used to study the role of pre-existing faults in compressive regimes. From a theoretical point of view, reactivation is mainly controlled by fault attitude, stress regime and frictional properties of fault planes. In scaled-down sandbox experiments, precut faults are introduced in the homogeneous granular media with a nylon wire which is forced through the sand cake producing a thin planar disturbed zone. Systematic experiments of thrust inversion with various dips and strikes of such planar discontinuities have been modelled. Comparison of experimental results with theoretical diagrams indicate that disturbed zones have a friction angle which is lo-20% lower than the homogeneous sand and that the compressive regime in the sandbox has a shape factor close to 0.4. The static analysis of fault reactivation is in accordance with the experimental observations except for pre-existing faults dipping at very low angle. However, numerical modelling using the Udec code shows that low-angle faults can be reactivated as a result of stress concentration in the lower part of the fault. In addition, sandbox experiments indicate that in thrust systems, reactivation of pre-existing faults is not only dependent on their attitude but also on their spacing and location relative to the thrust system.

Introduction Analogue modelling are extensively applied by both researchers from academia institutions and from the petroleum industry (Horsfield, 1980; Malavielle, 1984; Koopman et al., 1987; McClay and Ellis, 1987; Vendeville et al., 1991; Colletta et al., 1991). Physical scaled-down experiments allow to investigate some important deformation mechanisms responsible for the development of faults and structural style of sedimentary basins. In recent sandbox studies, models are analyzed in 3-D using X-ray tomography to visualize serial cross sections without destroying the models (Mandl, 1988; Colletta et al., 1991). With such a technique the complete kinematic evolution of the deformation can be recorded into video movies. As a first example of such a mode of analysis, studies of thin-skinned thrust structures have been published recently by Colletta et al. (1991). The authors performed model experiments of thrust propagation where horizontal layers of granular materials (sand and glass powder),

placed in the deformation box, were shortened by incremental displacement of a vertical backstop (Fig. 1). These thrust propagation experiments were found to be useful to reveal the importance of the factors affecting thrust spacing such as layer thickness (or depth to detachment), basal friction conditions, and also erosion. However, the geological data in many zones of folds and thrust belts often suggest that the structural inheritance in the form of various type of heterogeneities such as pre-existing arrays of faults, decollement horizons due to ductile materials (clay-evaporites) has important implications for the structural style (Butler, 1989; Letouzey, 1990). Ramp faults associated with thin-skinned overthrusting are often recognized as ancient normal faults which have been reactivated duiing compression. Furthermore, in weakly inverted areas like the English Channel or the Sunda platform in Indonesia, inverted grabens are those that are properly oriented with respect to shortening direction (Letouzey, 1990; Letouzey et al., 1990). Such examples illustrate the applicability of the

L

5Cm

o----

Fig. 1. Thrust propagation experiments analysed by successive tomographic images. In homogeneous material, spacing and attitude of thrusts is mainly controlled by basal friction conditions, internal friction angle of granular material and thickness of the sand The basal friction angle was lowered to cake. In this series of experiments, sand cake thickness was between 0.5 and 5 cm. approximately 20” by introducing a thin layer (about 1 mm thick) of glass microbeads at the bottom of the sand cake.

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basic principles of geomechanics to structural interpretation of seismic data. Analogue sandbox experiments on basin inversion probfems have been presented by McClay (19891, Buchanan and McClay (1991) and McClay and Buchanan (1992). The authors have documented the structural styles resulting from inversion of domino faulted systems or rollover extensional basins. The approach adopted in this study

(4

Stereonet projection Lower hemisphere

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proceeds in a different manner. We present a new series on thrust propagation experiments in which precut faults have been incorporated in the sand material. These precut faults are artificial dilation zones created using a nylon wire. We performed simple reactivation experiments with the objective to investigate the mechanical role of pre-existing faults in the case of thrusting along a detachment horizon. The series of sandbox tests

(b) Mohr circle representation

Fig. 2. (a) Theoretical diagrams of fault stability for five compressive states of stress with shape factor varying from 1 to 0. The stereonet diagrams display contour plots of the angle (Y= 25”. This contour line separates the domain where pole to the plane must be found for reactivation to occur (dark prey) from the domain where the pianes are stable (light grey). (b> Mohr circles representation for the various states of stress. 63 Correspondence between the pole to a fault plane (P, above) and its image in the Mohr circle envelope (P’, below).

W. SASS1 E-l‘ AL

Point P represent the pole to fault plane on the surface of the i unit sphere

x2

Shear stress ( .t) and normal stress (0.) on fault plane P given by P’ in the Mohr circle envelope T1, c

(C)

(after Wiebols and Cook, 1968)

Fig.2 (continued).

(extensional, strike-slip or compressional). It is generally admitted that before the creation of new faults, an ancient fault can be reactivated when its orientation with respect to the tectonic stresses is favorable and when the total resistance on the fault is less than the resistance to failure of the intact material. However, analysis of fault reactivation, in specific case studies, is complex because many geological factors may lead to a reduction of fault strength (Paterson, 1978), of which the most important one at basin scale is probably the fluid pressure (Zoback and Healy, 1984; Zoback et al., 1993-this issue). In the context of the present study, we are concerned with the modelling results of sandbox experiments in which the behaviour of the sand is described by a Coulomb failure criterion, i.e., a cohesionless granular material. Fault zones in the sandbox experiments correspond to, usually planar, zones of dilation called shear bands. The bulk density is decreased within the shear bands as a result of grain re-arrangements. Once created, we may assume that they form zone of weaknesses and that they may obey a Coulomb’s failure criterion like the undisturbed granular media. Therefore, it is expected that the difference in mechanical behaviour between a pre-existing fault in the sand and the intact material lies in the difference between the coefficient of friction of the fault zone (i.e., dilation zone in the sand) and that of the undisturbed sand.

are discussed in the light of the mechanical principles of fault reactivation (Sibson, 1974, 1985; Ranalli and Yin, 1990; Yin and Ranalli, 1992). Construction of fault stability diagrams Static analysis of fault reactivation Following the fault/ stress classification of Anderson (1905) and Bott (1959), analysis of the critical stress state capable to overcome the shear strength on a pre-existing fault has been described by many authors (Bott, 1959; Jaeger and Cook, 1979; Sibson, 1974, 1985; Ranalli and Yin, 1990; Yin and Ranalli, 1992). These works suggest that the most important factors are the fault plane orientation relative to the orientation of the stress axes, and the type of stress regime

Knowing the state of stress, theoretical diagrams of fault stability conditions can be constructed (Jaeger and Cook, 1979), as shown in Figure 2a and b where a Coulomb failure criterion is used to represent the shear strength for both the undisturbed granular media (angle of internal friction is taken to be equal to 30% and the artificial dilation zones (friction angle of 25”). Figure 2a shows the correspondance between the failure criterion, the type of stress tensor (here defined by the shape factor R, see below), and the orientations of the planes.

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Strike-slip

Compression Friction angle required to cause failure

Fig. 3. Stereonet diagrams showing a detailed representation of the contour plots of eqn. (6) for nine typical Andersonian stress states. These stress states correspond to extensional, strike-slip and compressional regimes with three distinct values of the shape factors R: 0.25, 0.5and 0.75. The different types of fault dispiacement to be expected are supe~m~sed on the diagrams: I = reverse faults; N = normal faults; S = sinistral faults; D = dextral faults. Combination of displacement is indicated by two letters (e.g. SZ = sinistrat-reverse fault).

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The theoretical diagrams shown in Figures 2 and 3 can be constructed as explained below. Let:

I 1 0

CT*

0

cry

0 0

c=

0

a,

0

be a given stress tensor with the principal stress directions parallel to the (x, y, z) orthogonal system of axes. We define the ratio of the principal differential stresses, also called the shape factor or simply the stress ratio, as: c2

R=_

-

Cl

fl3 -

*I

with U, = min(a,, a,,, a,); us = max(a,, or, a,), 0 < R < 1. By convention compressive stresses are taken to be negative in the computation. However, we refer to ot, uZ and us as being the maximum, intermediate and minimum principal compressive stresses, respectively. The stress vector applied on a plane of outward unit normal vector v, with direction cosines components (I, m, n) is:

with cr2 = crX212 + av2m2 + vz2n2. The normal stress vector is a, = (a. vlv, and the shear stress vector T = u - a,,:

r=

“(o;-0”)212+(~~-~“)2m2+(a,-a”)2n2 \i

(2)

The critical differential stress, ACT= (a, - a,>/2, responsible for the creation of a new fault zone in the granular material can be found using the Coulomb friction law: 7=

I.LfU”

(3)

where it = tg(4) and (b is the angle of (internal) friction for the undisturbed sand (we used 4 = 30”). The maximum differential shear stress Au, can be written as a function of the vertical stress, where a, = a, in the case of thrusting:

(4)

With eqn. (4), and a given R value, the three components of the stress tensor are defined by: (rZ=u3; a,=2Aa+cr_

and a,.=R(uZ-CJ-,)

+a,.

Here (and in Fig. 2b), ax = (TV stands for the maximum compressive stress and aY = U, is the intermediate principal stress. On the other hand, the Coulomb friction law for the existing fault zone gives: r = PLdo;l

(5)

where pLd= tg(4,) and 4d is the friction angle of the plane of weakness. The stereonet diagrams in Figure 2 display contour plots of the angle cy= 25”, where u is the angle between the resolved traction (a), and the unit normal to the plane (v): tg( a) = : II

(6)

which is a continuous function of (I, m, n), i.e., for all plane orientations with respect to the (x, y, z) coordinate system. The contour line. (Y= 25”, indicates the distribution in orientation of the pole to the planes verifying eqn. (5) (i.e. N = +d). This contour line separates the domain where the pole to the plane must be found for reactivation to occur (dark grey) from the domain where the planes are stable (light grey). Note that arbitrary values for the vertical stress a, can be used due to scale invariance of eqn. (6) by dilation in the deviator magnitude in the case of cohesionless frictional behaviour only. Equations (3) and (4) state the condition for a new fault to form with an orientation such as to contain the intermediate principal stress axis g2 and making an angle:

with the stress axis (T,. In each of the stress state represented in Figure 2b, there are two plane’s orientations verifying tg(a) = tg(&) = pr. The poles to those planes are located within the middle part of the reactivation domain in the stereonet diagrams of Figure 2b. The construction of such stereonet fault stability diagrams for all types of tectonic stress regime

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Fig. 4. Position of a new pop-up structure in sandbox experiments of imbricate thrusts propagation. The back thrust always merge at the surface close to the tip of the previous thrust. Due to basal friction stress trajectories are slightly deviated and the pop-up structure is inclined (after Mandl and Shippam, 1981).

Mobile backstop

Mapview

II

microbeads

sand /TJj$J glass powder

-Fig. 5. ~perimental

arU!i&l flagon me created using nylon wire

set up for sandbox experiments on fault reactivation. Cross section and map view showing various attitude of precut discontinuities.

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W. SASSI

can provide useful1 constraints for understanding the kinematics on pre-existing planes of weakness. In Figure 3 the stereonet diagrams show a more detailed representation of the contour plots of eqn. (5) for nine typical Andersonian stress states (i.e., one of the principal stress axis is parallel to the vertical direction). These stress regimes represent extensional, strike-slip and compressional stress states with assumed shape factors of 0.25, 0.5 and 0.75. The limiting stress state for the case of extensional and strike-slip

stress regime are fixed by relationships similar to eqn. (4). We have: for normal faulting and: PPZ

Au=

/.$(I - 2R) + /G for strike-slip faulting

Map view

Coeval development of a new “pop-up” structure.

Crosssectlon view

Map view

Fig. 6. Partial

reactivation

b’i- Al

of strongly

oblique

precut

fault.

/

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The different types of fault displacement to be expected are superimposed on the diagrams (angle between the resolved shear stress and the horizontal plane). Diagrams in Figure 3 highlight the relatively high variation of the fault reactivation domain as a function of the friction angle assumed for the fault zones. For a low friction angle of say lo”, the possible distribution of reactivated faults covers a large domain where as it is much reduced when sliding friction angle is larger than 20”. These diagrams may be used to further investigate fault reactivation problems in sandbox tests of compressional, extensional or strike-slip experiments. Fault reactivation experiments Thrust propagation experiments under homogeneous conditions as with the example of Figure 1, indicate that, for a given granular material (e.g., sand with internal friction angle of about 30”, grain size of 100 pm in average), the geometry of thrust imbrication depends mainly on the thickness of the sand layer and on the basal friction conditions (Fig. 4; Mandl and Shippam, 1981). The initiation stage of a new thrust imbrication starts with the development of a pop-up structure with two conjugate shear bands: a back thrust and a forward thrust with typical dip angles as shown in Figure 4 for low basal friction conditions. The two dilation planes strike perpendicular to the shortening direction. The apparent internal friction angle of the granular media is approximately equal to 30”. For low basal friction, a new pop-up structure will develop just in front of the previous thrust, such as the new back thrust will reach the surface at the tip of the previous forward thrust. Thus the distance at which a new pop-up develops can be predicted by simple geometrical relationship. In Figure 5a schematic representation of the modelling procedure adopted in this study of fault reactivation is given. To create a pre-existing plane of weakness a simple technique is used: a precut fault is introduced by carefully cutting the sand layer using a nylon wire which is 0.1 mm in diameter across. The disturbance produces a zone of less compacted grains. This zone called

TABLE 1 Modelling of structural complexity in sedimentary basins: the role of pre-existing faults in thrust tectonics Reactivated

Not reactivated Strike

Dip

Strike

Dip

10 10 13 20 20 21 21 31 40 50 50 50 50 50 60 65 65 75 75 90 90 90

51 77 45 14 53 32 76 16 47 20 45 53 56 85 53 51 55 55 70 45 56 75

30 30 40 40 50 50 50 50 50 50 60 65 65 65 75 75 90 90 90

35 90 20 40 16 19 24 30 38 55 30 10 36 60 30 45 10 30 46

the artificial dilation zone is found to reveal the same X-ray signature as the “natural” dilation zones which develop in thrust experiments (Fig. 1). In a first set of experiments a single fault was introduced in the model. Over 39 reactivation experiments of this type were conducted (Bale, 1990) to cover the widest range in fault orientations (both in strike and dip directions). A typical result of partial reactivation is illustrated in Figure 6. This is observed only for precut faults with a strong oblique orientation to shortening. For moderate displacement of the backstop, the whole dilation plane may be reactivated only when the fault strikes perpendicular to the shortening direction. The results of the whole series of fault reactivation tests are reported in Table 1 and plotted using the Schmidt lower hemisphere stereonet projection in Figure 7. A series of experiments was performed to test the role of spacing of the preexisting discontinu-

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ities. Thus, several precut faults, striking perpendicular to the shortening direction and dipping at about 30” were created. Figure 8a shows a cross section profile of a reactivated set of precut faults with an initial spacing allowing all faults to be reused whereas Figure 8b shows that only one fault in two can be reactivated when they are closely spaced. To be noticed in the documented experiments is that no back thrust develop during fault reactivation as compared with Figure 1. The results indicate that when the artificial dilation zone strikes perpendicular to the shortening di-

Exp&lmentaldata

set.

Fig. 8. Influence of spacing on precut fault reactivation. (a) In a widely spaced system, each discontinuity is rectivated. (b) In a closely spaced system, only one fault over two is reactivated.

0

Not reacUvnta+d

+

Readlvated

Reactlvstiondomain *

rection fault reactivation not only depends on the dip angle but also on the position of the faults within the thrust system.

Shortallhg

(Schmidt lower hemisphere projection of table I data set)

Fig. 7. Schmidt lower hemisphere projection of reactivated ( + ) and non-reactivated (0) precut discontinuities in sandbox experiments.

Interpretation

of the experimental

results

The data set in Figure 7 shows that precut faults that were reactivated have a specific orien-

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tation with the pole to the plane falling in a characteristic zone of the diagram. There is a well-defined boundary separating the reactivated from the non-reactivated precut faults. Overall, the results suggest that the apparent friction coefficient of the artificial dilation zones is lower than the internal friction (4 = 30”) required to created a new failure in the undisturbed sand. These experimental results may be compared with the prediction of a statically determined problem of fault stability conditions previously described. Indead, an average stress state with shape factor R of 0.4 best explains the whole set of reactivated fault planes as shown in Figure 9 in which one can compare the prediction of the static analysis with the experimental results. The angle (Yindicates which friction angle best fit the shape REACTIVATION BY COMPRESSION EXPERIMENTS ( Mohr - Coulomb Analysis ) 02

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of the pole distribution of the reactivated faults The upper limit in plane dip angle correlates with the 25” isoline. From Figure 9, the contour plots of cz show that 61% of the data set is enclosed in the 25” < (Y< 30” domain. An angle of 25” can therefore be considered to represent the apparent frictional angle for the precut planes. Data outside the static friction angle limit correspond to the low-angle-dipping precut faults. It is to be pointed out that the state of stress in Figure 9 is first of all an interpretation of the data in the light of theoretical consideration. This stress tensor represents an average state of stress that has a meaning only at a scale in space large enough to enclose the dimensions of the planes of weakness. The stress ratio indicates that the horizontal stress perpendicular to the shortening direction must be on average larger in magnitude than the vertical stress, since it represents the intermediate (a,) principal stress. All fault reactivation experiments were carried out independently, and the loading conditions correspond to uniaxial displacement of the sand package by the backstop. Fault dipping at a lower angle were found to be reactivated. Numerical modelling

02

Schmidt Stereonet projection ( lower hemisphere )

Fig. 9. Interpretation of the results of the sandbox experiments(see Table 1) with a static Mohr-Coulomb analysis.

Numerical experiments of fault reactivation are presented in Figures 10 and 11. The 2-D Distinct Element Method, (program UDEC version 1.7, Itasca, 1991; Cundall, 1980, 1989, 1990; Hart et al., 19881, is used here. This numerical method allows to describe a geological system as an ensemble of rigid and or deformable blocks. Faults are defined by the geometrical configuration of the block interfaces. Deformable blocks are discretized by a triangular mesh. Each triangle in the mesh is a domain where the stress state and the strain are constant. A Coulomb shear failure criterion is used to represent the critical shear strength along the block’s interfaces. The dimensions of the structures are given in Figure 10. In each model calculation, the basement and the mobile backstop are represented by rigid blocks and the overburden layer by two deformable blocks separated by a fault. The deformable blocks behave like linear isotropic elas-

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w SASSIEl Al

tic material. The friction angle is taken to be 25” along the fault and 20” along the entire basal decollement. Six models in which the fault cutting though the overburden layer dips at 60, 30, 20, 15, 10, and 5” in Figure IOa-f and lla-f, respectively, have been considered. These faults are imposed prior to application of a horizontal push of the mobile backstop. The same displacement (20 m) is applied to the backstop in the six

c

models and gravity is taken into account. Figure lla-f, display the stress fields in the vicinity of the faults after application of 20 m displacement of the backstop. With an elastic behaviour we obtain the Largest heterogeneity in the stress field as shown for example in Figure 11, involving rapid rotation of the principal stress axis as well as rapid change in stress intensity. This stress pattern builds up be-

12 km

a

b

d

Fig. 10. Numerical modelting of fault reactivation using the distinct element method. Upper part show the geometry of the model. (a-f) show the magnitude of shear displacement (proportional to line thickness), along the discontinuities (basal decollement and the faults when reactivated), after 20 m displacement of the backstop towards the right. Dip of pre-existing fault is 60” (a), 30” (b), 20” (c), 15” Cd), IO”(e) and 5” (f).

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cause the thrusted blocks are uplifted leading to a partial opening of the basal de~llement in front of the fault cutoff point (Fig. lClb-f).

The model’s results suggest the following remarks: 64) As expected from static considerations, 1 km

principal str0sses minimum = -8575E+04 maximum= 1.319E+O3 I 0

I

I

1

1

I 5E E

_0.250 0

principal stresses minimum = -3.570E+O5 maximum= 2.~*~+04

principal stresses minimum I -3.514Ei05 maximum= l.G7OE+O4 I,,,,,,l,lI,,,,,,,,,( 0

2E 6

1

_

._ ..

._. . _-.. 5 . . . .. . -. . . .. ._ _

.

.

.

\*,*

-.\ \-. .

I\‘,. . .

.

.

0750

_‘.

. “ _.__

\.*_

_ _

.” _.

_-

km

-__-

. _-_-

__

.

_*_-

.

. _-

. .

*.

.__ .

_ 0 250

0

principal stresses minimum = -3.392E+05 maximum= l.l03E+O4

principal stresses minimum = -3.208E+05 maximum= 7.036E+O3

principal stresses minimum = -2.906Ei05 maximum= 4.712E+O3

1

km

Fig. 11. Numerical modelling of fault reactivation using the distinct element method code UDEC: display of the stress fields resulting from horizontal compression by displacement of a mobite backstop from left to right (same calculation as shown in Fig. lOa-f). Dip of pre-existing faults is 60” (a), 30” (b), 20” Cc), 15” Cd), 10” (e) and 5” (f).

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the steep fault with 60” dip (Fig. 10a) is found to be stable. In Figure lla the displacement along the whole base of the structure decreases from left (20 m) to right (14 m). In this case the stress field pattern is qualitatively analogue to the stress distribution derived using the analytical solution of Hafner (1951). (B) In the areas near the base of all the reactivated faults, stress perturbation occurs as a result of uplift of the thrusted blocks. The best orientated fault plane (30” dip), is strongly reactivated and display the widest variation of the stress field in the thrusted block. (0 The stress variations, both in direction and intensity, around the faults are responsible for the reactivation of the low-angle dipping faults. It is important to note that this result shows that the assumption of an Andersonian stress state is not valid here: whatever the magnitude of the stress deviator, the failure criterion cannot be matched for a fault dipping at Y, with a coefficient of sliding friction of 25” and with or without cohesion term. Various aspects of stress trajectories and fault reactivation can be studied using analytical (Hafner, 1951) or numerical modelling (e.g., Walters and Thomas, 1982; Maekel and Walters, 1993-this issue). Here, the model’s results are useful to illustrate how pre-existing faults may influence the distribution of stresses as a result of loading by horizontal compression. We adopted the simple case of linear elasticity for the deformable overburden rocks. However, assuming a different rheological material law such as a Bohr-Coulomb plasticity criterion would yield a slightly modified stress pattern, showing plastic failure where the largest stress concentrations occurs in the system. The zone of plastic failure may suggest either the fracturing of the overburden material, of if Iocalized the initial development of a new fault. However, the two mechanisms, new failure in the intact rock mass or reativation of an acient fault, may operate at the same time. This will essentially depend on the difference between the total resistance to failure of the intact rock mass and the resistance to failure along the preexisting fault surface.

Conclusions

Structural style of compressional basins may be strongly influenced by the existence of faults acquired prior to compressive tectonism. Previous work using field studies and map view of geological structures have suggested that the main factors ~ontroIling basin inversion structures are the relative orientation of the inherited faults and the superimposed regional tectonic stress field. This is supported by theoretical analysis of stability conditions on faults given the tectonic stress field and adopting a failure criterion to formulate the static equilibrium conditions. In this paper, the mechanics of fault reactivation by compressional loading has been further investigated, based on the results of sandbox experiments. In these experiments, the reactivation of the precut faults introduced in the granular media yields a consistent pattern illustrating the applicability of theoretical predictions. The analysis of the experimental results indicates that the effective friction coefficient of the artificial dilation zones is lower than that of the undisturbed media. The compressive regime that best explains the observed experimental reactivation pattern corresponds to an average stress state with a shape factor of 0.4, assuming an effective friction angle of 25” for the frictional property of the precut faults. The static Mohr-Coulomb analysis does not explain the observed reactivation of some low angle faults but numerical modelling of a similar problem in 2D show that reactivation may occur as a result of local stress perturbation and rotation in the system. Eventhough artificial and natural shear bands have lower effective friction coefficient compared to the undisturbed media, faults that are well orientated with respect to the overall stress field are not neccessarily reactivated as illustrated in the case of varying the spacing of periodic fault pattern. On the other hand, some of the experiments suggest that with thin-skinned tectonic compression, oblique faults relative to compression may be re-used with simultaneous development of new thrust imbrications. The expression of such defo~ation mechanisms as a result of geometric and mechanical factors show

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that the present technique can be used to treat more complex problems of structural interpretation and to study the relationship between faulted basins and stress regimes. Acknowledgements

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